Fungrim entry: 8f5e66

\zeta\!\left(s\right) = \prod_{p \in \mathbb{P}} \frac{1}{1 - \frac{1}{{p}^{s}}}

Assumptions:

s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(s\right) \gt 1

TeX:

\zeta\!\left(s\right) = \prod_{p \in \mathbb{P}} \frac{1}{1 - \frac{1}{{p}^{s}}}

s \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Re}\!\left(s\right) \gt 1

Definitions:

Fungrim symbol	Notation	Short description
`RiemannZeta`	$\zeta\!\left(s\right)$	Riemann zeta function
`Pow`	${a}^{b}$	Power
`PP`	$\mathbb{P}$	Prime numbers
`CC`	$\mathbb{C}$	Complex numbers
`Re`	$\operatorname{Re}\!\left(z\right)$	Real part

Source code for this entry:

Entry(ID("8f5e66"),
    Formula(Equal(RiemannZeta(s), ProductCondition(Div(1, Sub(1, Div(1, Pow(p, s)))), p, Element(p, PP)))),
    Variables(s),
    Assumptions(And(Element(s, CC), Greater(Re(s), 1))))

Topics using this entry

Riemann zeta function

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC